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Discrete Choice Methods
with Simulation
h E. Train
University of California, Berkeley
and
National Economic Research Associates, Inc.
iii
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To
Daniel McFadden
and
in memory of
h Train, Sr.
ii
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Discrete Choice Methods with Simulation
This book describes the new generation of discrete choice meth-
ods, focusing on the many advances that are made possible by
simulation. Researchers use these statistical methods to examine
the choices that consumers, households, firms, and other agents
make. Each of the major models is covered: logit, generalized
extreme value (including nested and cross-nested logits), probit,
and mixed logit, plus a variety of specifications that build on
these basics. Simulation-assisted estimation procedures are
investigated pared, including maximum simulated
likelihood, the method of simulated moments, and the method
of simulated scores. Procedures for drawing from densities
are described, including variance reduction techniques such
as antithetics and Halton draws. Recent advances in Bayesian
procedures are explored, including the use of the Metropolis–
Hastings algorithm and its variant Gibbs sampling. No other
book incorporates all these topics, which have risen in the past
20 years. The procedures are applicable in many fields, includ-
ing energy, transportation, environmental studies, health, labor,
and marketing.
Professor h E. Train teaches econometrics, regulation,
and anization at the University of California,
Berkeley. He also serves as Vice President of National Economic
Research Associates (NERA), Inc. in San Francisco, California.
The author of Optimal